Plumbing in new addition question.

Hi, Larry here. Im starting the plumbing in a new addition. Im asking if I can vent a shower stall and toilet with a 2" vent. The shower stall and toilet line up in the same basment joist bay 7.5' apart. I was going to come down the back wall with the vertical 2" dry vent which goes directly up and out roof, 90 degree into the basement joist, go 1' and covert to 3" waste. From that point go 1' more and wye in the shower trap. From shower trap 5.5' to 3" toilet and wye in with 3". From there 1.5' and wye into the main soil line going out. Basiclly everthing lines up in a row with the vent starting in the back and direction of flow going towards the toilet. Hope this makes some sense. Thanks for all your help.